Using JMP software, if my dependent variable on the y-axis is a continuous variable "Revenue from Movie" and the predictors are 4 categorical variables ( 1= Action, 2=Comedy, 3 = Kids, 4=Other) then I find that the JMP software always leaves one of the 4 categorical variables out in the regression output.
The least squares mean of the left out variable becomes the intercept on y-axis and then every other regression co-efficient is interpreted with respect to this intercept (the least squares mean of the left out variable). In some way, I see this gives the same information with fewer variables because the R-square does not change but why does it work this way. That's what I dont understand. How come everything is interpreted with respect to what we left out and we still have the same R-square.
In this image, we left out "Kids" so its least squares mean becomes the intercept and then Action = 56.66 - 45.10 = 11.56 and so on
